About 25 percent of Dominos' sales are already coming from smartphones, and another 25 percent are coming from other digital sources.

Dominos is ahead of the game on smartwatch ordering as well, as the company has already launched a smartwatch app that allows pizza ordering and tracking from Pebble and Google Inc (NASDAQ: GOOG) (NASDAQ: GOOGL)'s Android smartwatches.

Papa John's hasn't specifically mentioned plans for an Apple Watch app. However, the company recently began accepting Google Wallet as a payment method and has expressed interest in adding other payment options as well.